If electrons were positive and protons were negative, would life be different? This was a question on a worksheet during my first week in a class on Electromagnetism. The answer is essentially:

No. Life would be no different if electrons were positively charged and protons were negatively charged. Opposite charges would still attract, and like charges would still repel. The designation of charges as positive and negative is merely a definition.

But how would we have negative charges within the nucleus? Taking a look at the Wikipedia page for residual strong force, it seems that down quarks are required in this new "negative proton" to help with creating the pion to "transmit a residual part of the strong force even between colorless hadrons".
I tried to set out and try to find a particle with (-1) charge with a down quark (by going through this list of baryons) but all the particles are not stable with the exception of two unknown:


*

*Bottom Xi Baryon

*Double Bottom Xi Baryon
Assuming one of the above are stable, could the strong force act between one of them and a neutron, implying its alright to have a negatively charged nucleus?
Edit: If it wasn't clear, my question concerned whether or not there existed stable baryons of $-1$ charge with down quarks that could "replace" the proton.
 A: The positive and negative charges assigned to protons and electrons respectively are by convention. There is no specific reason for making the electron negative. Just like gluons have colour charge, similarly in order to show that there are particles similar to the electron which rebel each other,  they've been marked as negative charge. They could have been easily marked positive as well.
Had the electrons been positive and protons been negative, then physics would have to be formulated like that. Quarks would have to change their charge, so that they would add up to a unit negative charge of the proton. However, all phenomena could be described by that system, just like they're described by the current system. Only the signs of all would change.
A: The point is that whether we call it 'positive' charge or 'negative' charge makes no difference, as long as we are consistent. If we decided to label the charge of a proton as 'negative' then, to be consistent, we must also relabel the charges of the quarks (i.e. d would become +1/3e, and u would become -2/3e). In which case your question is void.
A: As for your question on how to get negative charges in the nucleus, this is easy. Just use anti-protons (and anti-neutrons). The formers quark content is simply $\bar{u}\bar{u}\bar{d}$, so it consists of two anti-up and one anti-down quark. The charge of an anti-up quark is the opposite of that of an up-quark, so -2/3 and, analogously, +1/3 is the charge of an anti-down quark.
To make atoms with this, you also need to replace electrons with their respective anti-particles, which are called positrons, named so because they have +1 charge.
Whether or not matter made from the anti-particles of our normal matter really behaves in exactly the same way is a hot topic and under active research. We know that there are at least a few small differences; and from observing that we are made from matter, not antimatter, there must be even more differences we do not understand yet.
So, depending on how one interprets the question, yes there are differences if you replace all positive charges with negative ones and vice versa. It depends on how you do it.
However, it was recently shown that the spectrum of hydrogen and anti-hydrogen is the same (within experimental uncertainties).

Side note: if you only exchange charges, but don't do a parity transformation (basically mirroring all spatial directions), lone charges will be deflected in opposite directions in a magnetic field from what you are used to.
